تعادل در بازار برق لحظه ای و آتی

We describe a model to analyze the equilibrium encompassing an electricity futures market and a number of electricity spot markets sequentially arranged along the time horizon spanned by the futures market. Profit-maximizing strategic electricity producers react to both prices and rival production changes, in both the spot and the futures markets. At each time period, the total demand is considered to depend linearly on the spot price of the considered time period, and the futures market price is assumed to equal the average spot price over the time horizon. Equilibrium conditions at each spot market are described as a function of the futures market decision variables, which in turn allows describing the equilibrium in the futures market implicitly enforcing equilibrium in each spot market. The proposed model allows deriving analytical expressions that characterize such multi-market equilibrium and that can be recast as a mixed linear complementarity problem. This model is useful to gain insight on the outcomes and characteristics of the considered multi-market equilibrium. Such insight may allow the regulator to better design the futures and spot trading floors, their rules and sequential timing. It may also allow producers to increase the effectiveness of their respective offering strategies.

As electricity markets mature throughout the world, futures markets become more and more liquid and relevant for electricity trading. This is the case, for instance, of EEX [1] in Central Europe or NYMEX [2] in the East Coast of the US. Futures markets allow trading products (mainly forward contracts and options) spanning a large time horizon, e.g., 1 month, while spot markets are typically cleared on an hourly basis throughout the time periods spanned by the futures market products. Thus, futures and spot markets interact and such interaction results in multi-market equilibria. It is important to note that a futures market equilibrium generally encompasses a large number of spot market equilibria. As an example, consider different peak and base forward contacts (futures market products) spanning, for instance, the month of May. An electricity producer may sell its production using such contracts or, alternatively, through the 31 × 24 hourly spots markets spanning May. The producer may also sell part of its energy production through forward contracts and the remaining energy in the successive spot markets. The profit-seeking interaction of all producers (strategic or otherwise) within the futures market and the spot markets being cleared during the time horizon defined by the forward contracts does characterize the market equilibria. Following the practice in some real-world markets, we consider a single futures market that is cleared prior to the subsequent spot markets. Therefore, the quantities sold by each producer in the futures market are delivered in the spot markets without any possibility of continuous renegotiation. Within the above market framework, we consider strategic electricity producers that react through conjectural variation (CV) models to both the spot prices and the productions of rival producers in both the futures and the spot markets. This characterization of strategic producers is flexible enough to analyzed different types of market competition, including Cournot competition, the formation of cartels by groups of producers, monopoly and perfect competition. At each time period, the total demand (supplied through futures market products and the spot) is considered to depend linearly on the spot price of the considered time period. Moreover, the average spot price (computed as the arithmetic mean over time of the spot prices) is assumed to be equal to the futures market price, i.e., the risk premium is assumed to be nil. This is an assumption consistent with empirical observation in different energy markets. Equilibrium conditions at each spot market are described as a function of the futures market decision variables (futures market price and the energy sold in the futures market by each producer), which in turn allows describing the equilibrium in the futures market implicitly enforcing equilibrium in each spot market. The result is a so-called multi-market equilibrium, and involves the futures market price, hourly spot prices, and the energy sold in the futures and each spot market by each producer. The proposed model allows deriving analytical expressions, equalities and inequalities, that characterize the multi-market equilibrium and that can be recast as a mixed linear complementarity problem, MLCP, easily solved using available software, e.g., PATH [3] under GAMS [4]. Observe that the model described in the paper does not represent the network since representing it makes intractable the proposed analytical approach. If the network needs to be represented, a numerical instead of an analytical approach needs to be used, as for instance in [39]. However, note that an analytical approach provides insights that computational approaches cannot provide. It is relevant to note that congestion issues can be handled through a post market procedure as reported, for instance, in [6]. Please, note that this is the actual practice in most European markets, as the Iberian Peninsula market [7], or EEX in Germany [1].

This paper provides an electricity equilibrium model involving a futures market and a collection of successive spot markets within the time span of the considered future derivatives. The conclusions below are in order: 1 Under mild simplifying assumptions, analytical results in the form of an MLCP can be derived to characterized the multimarket equilibria. The analytical results obtained are applied to a market involving different competition levels: monopoly, cartel, conjectural variation, Cournot and perfect competition. 2 Within the considered multi-market framework, Alaz and Vila results reported in [11] are verified. Furthermore, futures markets are more effective to decrease market prices as the producers behave more competitively. 3 As expected, higher competition implies lower prices and lower profits for producers. 4 There are some market situations in which a power producer may not be inte